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1 IntroductionThe terminology of "fuzzy logic" has been formed and employed with different meanings by a large number of researchers soon after Zadeh published his initiate paper (see [1]), but perhaps the most serious work on fuzzy logic is the Pavelkas series papers (see [2]) which provided a systematical theory of fuzzy logic mathematically and profoundly, and hence has been accepted by scholars as a standard theory in developing their researches on fuzzy logic. Recently, Wang Guojun proposed a new fuzzy propositional deduction system (ζ)* (see [3]), and certain kind of logic foundation for the theory of fuzzy reasoning has been provided therefrom (see [4-7]). It is no doubt valuable if one combines Wangs work with Pavelkas theory,and the aim of this paper is to do so. In the present paper, the system (ζ)* has been extended both syntactically and semantically, an extension sequence {(ζ)*n} has been formed based on the revised finite-valued Kleene logic systems,especially, the semantical completeness has been proved for each of the above mentioned systems. These results reflect the advantages of the system (ζ)* and some more serious logic foundation for the theory of fuzzy reasoning could be expected therefrom.